Privileged-context on-policy self-distillation degrades thinking models' long-budget accuracy by suppressing forking and self-correction behaviors, while helping instruction-tuned models.
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arXiv preprint arXiv:2411.19943 , year =
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abstract
Mathematical reasoning tasks pose significant challenges for large language models (LLMs) because they require precise logical deduction and sequence analysis. In this work, we introduce the concept of critical tokens -- elements within reasoning trajectories that significantly influence incorrect outcomes. We present a novel framework for identifying these tokens through rollout sampling and demonstrate their substantial divergence from traditional error tokens. Through extensive experiments on datasets such as GSM8K and MATH500, we show that identifying and replacing critical tokens significantly improves model accuracy. We propose an efficient methodology for pinpointing these tokens in large-scale datasets using contrastive estimation and extend this framework to enhance model training processes with direct preference optimization (DPO). Experimental results on GSM8K and MATH500 benchmarks with the widely used models Llama-3 (8B and 70B) and Deepseek-math (7B) demonstrate the effectiveness of the proposed approach, cDPO. Our results underscore the potential of leveraging critical tokens to reduce errors in reasoning tasks, advancing the development of AI systems capable of robust logical deduction. Our code, annotated datasets, and trained models are available at https://github.com/chenzhiling9954/Critical-Tokens-Matter to support and encourage future research in this promising field.
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ICT framework applies JS divergence to token logits to select critical tokens for selective RLVR updates, claiming 4.58% average pass@4 gains on Qwen2.5 models across seven reasoning benchmarks.
EGPS localizes MCMC moves to high-entropy decision points using forward-pass entropy, yielding up to 12.6× wall-clock speedup and best-or-tied accuracy on MATH500, HumanEval, and GPQA for Qwen2.5-Math-7B.
POISE trains a lightweight probe on the actor's internal states to predict expected rewards for RLVR, matching DAPO performance on math benchmarks with lower compute by avoiding extra rollouts or critic models.
Standard top-k routers in MoE language models often select suboptimal routes for difficult tokens, and updating only the final router layer raises pass@K on AIME and HMMT benchmarks across multiple models.
AGDO improves dLLM reasoning performance by determining denoising order and emphasizing tokens based on attention-derived dependencies rather than random masking.
The L2 norm of LLM hidden states signals reasoning intensity, with a theoretical bound on SAE feature activations, enabling three new test-time scaling techniques that boost performance.
Smaller models provide temporally correlated policy-level diversity that serves as structured exploration for training larger models in GRPO, yielding accuracy gains such as +8.8% on AIME 24 with reduced compute via the S2L-PO framework.
AttentionPO weights tokens in DPO using LLM attention as a pairwise judge, yielding better results on AlpacaEval, MT-Bench, and ArenaHard than prior preference optimization methods.
InsightReplay improves long CoT reasoning by extracting critical insights from the trace and replaying them near the active frontier, delivering +1.65 average accuracy gain across 24 model-benchmark settings.
HTPO introduces hierarchical token-level objective control in RLVR to balance exploration and exploitation by grouping tokens according to difficulty, correctness, and entropy, yielding up to 8.6% gains on AIME benchmarks over DAPO.
AtManRL learns an additive attention mask on CoT traces to produce a saliency reward that, when combined with outcome rewards in GRPO, trains LLMs to generate reasoning that genuinely influences final predictions.
High-entropy minority tokens drive RLVR gains, so restricting gradients to the top 20% maintains or improves performance over full updates on Qwen3 models, especially larger ones.
HAB applies coarse-to-fine budgeting to LLM reasoning, predicting per-problem depth and learning intra-step token budgets via PPL comparisons and adaptive Pareto optimization, yielding higher accuracy and lower token use than standard CoT on GSM8K and MATH500.
Select to Think reframes LLM help as ranking among SLM top-K candidates and distills the ranking ability back into the SLM for improved single-pass reasoning.
citing papers explorer
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Rethinking On-Policy Self-Distillation for Thinking Models
Privileged-context on-policy self-distillation degrades thinking models' long-budget accuracy by suppressing forking and self-correction behaviors, while helping instruction-tuned models.
-
Beyond Entropy: Learning from Token-Level Distributional Deviations for LLM Reasoning
ICT framework applies JS divergence to token logits to select critical tokens for selective RLVR updates, claiming 4.58% average pass@4 gains on Qwen2.5 models across seven reasoning benchmarks.
-
Sample Where You Struggle: Sharpening Base Model Reasoning via Entropy-Guided Power Sampling
EGPS localizes MCMC moves to high-entropy decision points using forward-pass entropy, yielding up to 12.6× wall-clock speedup and best-or-tied accuracy on MATH500, HumanEval, and GPQA for Qwen2.5-Math-7B.
-
Your Language Model is Its Own Critic: Reinforcement Learning with Value Estimation from Actor's Internal States
POISE trains a lightweight probe on the actor's internal states to predict expected rewards for RLVR, matching DAPO performance on math benchmarks with lower compute by avoiding extra rollouts or critic models.
-
When Are Experts Misrouted? Counterfactual Routing Analysis in Mixture-of-Experts Language Models
Standard top-k routers in MoE language models often select suboptimal routes for difficult tokens, and updating only the final router layer raises pass@K on AIME and HMMT benchmarks across multiple models.
-
Beyond Fully Random Masking: Attention-Guided Denoising and Optimization for Diffusion Language Models
AGDO improves dLLM reasoning performance by determining denoising order and emphasizing tokens based on attention-derived dependencies rather than random masking.
-
The Tell-Tale Norm: $\ell_2$ Magnitude as a Signal for Reasoning Dynamics in Large Language Models
The L2 norm of LLM hidden states signals reasoning intensity, with a theoretical bound on SAE feature activations, enabling three new test-time scaling techniques that boost performance.
-
Smaller Models are Natural Explorers for Policy-Level Diversity in GRPO
Smaller models provide temporally correlated policy-level diversity that serves as structured exploration for training larger models in GRPO, yielding accuracy gains such as +8.8% on AIME 24 with reduced compute via the S2L-PO framework.
-
Token-weighted Direct Preference Optimization with Attention
AttentionPO weights tokens in DPO using LLM attention as a pairwise judge, yielding better results on AlpacaEval, MT-Bench, and ArenaHard than prior preference optimization methods.
-
Stateful Reasoning via Insight Replay
InsightReplay improves long CoT reasoning by extracting critical insights from the trace and replaying them near the active frontier, delivering +1.65 average accuracy gain across 24 model-benchmark settings.
-
HTPO: Towards Exploration-Exploitation Balanced Policy Optimization via Hierarchical Token-level Objective Control
HTPO introduces hierarchical token-level objective control in RLVR to balance exploration and exploitation by grouping tokens according to difficulty, correctness, and entropy, yielding up to 8.6% gains on AIME benchmarks over DAPO.
-
AtManRL: Towards Faithful Reasoning via Differentiable Attention Saliency
AtManRL learns an additive attention mask on CoT traces to produce a saliency reward that, when combined with outcome rewards in GRPO, trains LLMs to generate reasoning that genuinely influences final predictions.
-
Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning
High-entropy minority tokens drive RLVR gains, so restricting gradients to the top 20% maintains or improves performance over full updates on Qwen3 models, especially larger ones.
-
Thinking Economically: A Hierarchical Framework for Adaptive-Complexity Reasoning in LLMs
HAB applies coarse-to-fine budgeting to LLM reasoning, predicting per-problem depth and learning intra-step token budgets via PPL comparisons and adaptive Pareto optimization, yielding higher accuracy and lower token use than standard CoT on GSM8K and MATH500.
-
Select to Think: Unlocking SLM Potential with Local Sufficiency
Select to Think reframes LLM help as ranking among SLM top-K candidates and distills the ranking ability back into the SLM for improved single-pass reasoning.
- The Periodic Table of LLM Reasoning: A Structured Survey of Reasoning Paradigms, Methods, and Failure Modes